The difference between how the texture looks as a stand-alone image and inside a 3D scene is caused by different lighting conditions. When you look at the stand-alone texture it’s displayed as-is, but when you look at it inside the scene, it’s illuminated with light sources in the scene. Shapespark light sources use colors corresponding to real-world: sky light is cool-blueish, while sun light and artificial light is warm-yellowish. Furthermore, when a light bounces off a surface, the bounced rays get colored with the surface color.
If you need to make the texture look similar to the stand-alone version you can change color of all light sources to white. Or, if it’s not a problem that the texture stands out in terms of illuminatino, you can disable the lightmap for the object, by setting Custom lightmap resolution to 0 (requires re-bake), and perhaps making the material a bit emissive.